(2x-1)(2x-1)-16=0

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Solution for (2x-1)(2x-1)-16=0 equation: 


Simplifying
(2x + -1)(2x + -1) + -16 = 0

Reorder the terms:
(-1 + 2x)(2x + -1) + -16 = 0

Reorder the terms:
(-1 + 2x)(-1 + 2x) + -16 = 0

Multiply (-1 + 2x) * (-1 + 2x)
(-1(-1 + 2x) + 2x * (-1 + 2x)) + -16 = 0
((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) + -16 = 0
((1 + -2x) + 2x * (-1 + 2x)) + -16 = 0
(1 + -2x + (-1 * 2x + 2x * 2x)) + -16 = 0
(1 + -2x + (-2x + 4x2)) + -16 = 0

Combine like terms: -2x + -2x = -4x
(1 + -4x + 4x2) + -16 = 0

Reorder the terms:
1 + -16 + -4x + 4x2 = 0

Combine like terms: 1 + -16 = -15
-15 + -4x + 4x2 = 0

Solving
-15 + -4x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -2x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-1.5, 2.5}

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